A331422 - OEIS

A331422

Triangle T(n, k) of the number of connected graphs of order n with cutting number k >= 0.

1, 1, 1, 1, 3, 0, 2, 1, 10, 0, 0, 5, 3, 2, 1, 56, 0, 0, 0, 29, 0, 13, 8, 3, 2, 1, 468, 0, 0, 0, 0, 219, 0, 0, 63, 69, 0, 16, 12, 3, 2, 1, 7123, 0, 0, 0, 0, 0, 2706, 0, 0, 0, 502, 263, 300, 0, 85, 80, 24, 16, 12, 3, 2, 1, 194066, 0, 0, 0, 0, 0, 0, 52879, 0, 0, 0, 0, 6191, 3197, 0, 2148, 861, 632, 319, 352, 132, 160, 80, 24, 21, 12, 3, 2, 1

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OFFSET

1,5

COMMENTS

The cutting number of a node v in a graph G is the number of pairs of nodes {u,w} of G such that u!=v, w!=v, and every path from u to w contains v. The cutting number of a connected graph, is the maximum cutting number of any node in the graph.

LINKS

Sean A. Irvine, Rows n = 1..12 flattened

Sean A. Irvine, Java program (github)

Simon Mukwembi and Senelani Dorothy Hove-Musekwa, On bounds for the cutting number of a graph, Indian J. Pure Appl. Math., 43 (2012), 637-649.

EXAMPLE

The triangle begins:

1, 1;

3, 0, 2, 1;

10, 0, 0, 5, 3, 2, 1;

56, 0, 0, 0, 29, 0, 13, 8, 3, 2, 1;

468, 0, 0, 0, 0, 219, 0, 0, 63, 69, 0, 16, 12, 3, 2, 1;

...